Multiple conditional asynchronous recursive functions and jQuery promises

I have a complicate recursive javascript function that worked very well until I needed to start using asynchronous functions (jQuery.ajax in this case). I have included some psuedo-code below that gives the gist of the situation. I would like to implement this code using promises (instead of the current callbacks), but can't work out how to do deal with the recursion and the multiple conditional ajax calls. If I understand promises correctly they allow you to act on the return of an asynchronous call, but how do I deal with the situation below?

function wrapperFunction(success,error) {
    var level = 0;
    result = [];

    var innerFunction = function(info,result,success,error) {
        level++;

        jQuery.ajax({
            url: 'baseurl1' + info,
            success: parseData,
            error: error
        });

        function parseData(data) {
            data.forEach( function(item) {
                result.push(item.something);

                if ( item.info ) {
                    innerFunction(item.info, result, success, error);
                }
            });

            if ( data.condition ) {
                jQuery.ajax({
                    url: 'baseurl2' + info,
                    success: parseData2,
                    error: error
                });
            }

            function parseData2(data2) {
                data2.forEach(function(item2) {
                    if ( item2.condition ) {
                        jQuery.ajax({
                            url: 'baseurl3' + info,
                            success: parseData3,
                            error: error
                        });
                    }
                });
                function parseData3(data3) {
                    if ( data3.condition ) {
                        jQuery.ajax({
                            url: 'baseurl4' + info,
                            success: parseData4,
                            error: error
                        });
                    }
                    function parseData4(data) {
                        result.push(data2.something + data4.something);
                    }
                }
            }

            level--;
            if (level == 0 && success) {
                success(result);
            }
        }

    }

    innerFunction('rootinfo', result, success, error);   
}   

wrapperFunction(
    function(data) {
        // process success
    },
    function(err) {
        // handle errors
    }
}

As I said already, this is only pseudo code. I initially extracted it from my real code to see if I could get my head around the actual structure. I know it works if the ajax calls where synchronous, but now they are asynchronous it only sometimes works (depending on how quickly the calls return).

How do I implement this situation using promises?

EDIT

I have just worked out how to use promises to serialise everything, and though that is one way to wait for everything to finish I rather run multiple calls in parallel and then find a way to wait for everything to finish. I know this is possible with promises, but I don't know how.